Complex Systems

Academic year
Subject Area
Biomedical Engineering
Language of Instruction
Other Languages of Instruction
Mode of Delivery
ECTS Credits
2nd Cycle Studies - Mestrado

Recommended Prerequisites

Introduction to Artificial Intelligence, Evolutionary Computation.

Teaching Methods

Lectures: theories and methods used in heuristic problem solving. Students solve in practical classes computer problems of medium complexity and by means of simulations using particular frameworks. This is a group work done under the supervision of the professor. Written synthesis of a recent research work, experimental work involving computer simulations, done individually and includes a written report and an oral presentation.

Learning Outcomes

The main goal of this course is the study of complex system, either physical (e.g., the weather), biologic (e.g., genetic regulatory networks), cognitive (e.g., the mind) or social (e.g., the stock market). We will be focused on the concepts, the models and the tools necessary to the comprehension of these systems. We will start with a conceptual discussion involving the notions of system, complexity, self-organization, emergency, information, computation and evolution. Then, we will proceed with a description of different classes of models of complex systems. We will end with the presentation of different tools and frameworks and several case studies. In the end ,the student will be able to choose the right model and the appropriate tool to analyze a complex system, and extract knowledge from that analysis.

Work Placement(s)



1. Concepts (system, complex system, complex adaptive system, dynamic system, complexity and diversity, information, computation, evolution and models).

2. Mathematical models (cellular automata, fractals, chaos, self-organized criticality)

3. Network models (small-world, scale-free, random Boolean)

4. Rule Based models (collective intelligence)

5. Tools and frameworks

6. Case Studies.

Assessment Methods

Synthesis work: 10.0%
Project: 30.0%
Exam: 60.0%


1. Nino Boccara, Modeling complex systems, Springer, 2004.

2. Allen B. Downey, Think Complexity, O’Reilly, 2012.

3. Gary Flake, The computational beauty of nature: computer expçorations of fractals, chaos, complex systems and adaptation, MIT Press, 1998.

4. John H. Miller and Scott E. Page, Complex Adaptive asystems: an introduction to computational models of social life, Princeton University Press, 2007.

5. Melanie Mitchell, Complexity: a guided touer, Oxford University Press, 2009.

6. Scott E. Page, Diversity and Complexity, Princeton University Press, 2011.

7. Heinz-Otto Peithgen, Harmut Juergens, and Dietmar Saupe, Chaos and Fractals: new frontiers of science (2nd Edition), Springer, 2004.

8. Daniel Shiffman, The Nature of Code, 2012.

9. Ricard Solé and Brian Goodwin, Signs of Life: how complexity pervades biology, Basic Books, 2000.